On many of the staple measures of comparative psychology, elephants show no obvious differences from other mammals, such as primates: discrimination learning, memory, spontaneous tool use, etc. However, a range of more naturalistic measures have recently suggested that elephant cognition may be rather different. Wild elephants sub-categorize humans into groups, independently making this classification on the basis of scent or colour. In number discrimination, elephants show no effects of absolute magnitude or relative size disparity in making number judgements. In the social realm, elephants show empathy into the problems faced by others, and give hints of special abilities in cooperation, vocal imitation and perhaps teaching. Field data suggest that the elephant’s vaunted reputation for memory may have a factual basis, in two ways. Elephants’ ability to remember large-scale space over long periods suggests good cognitive mapping skills. Elephants’ skill in keeping track of the current locations of many family members implies that working memory may be unusually developed, consistent with the laboratory finding that their quantity judgements do not show the usual magnitude effects.